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Abstract
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The multiple multipoles (MMP) method is used to solve a nonlinear eigenvalue problem for
analysis of a 2D metallic and dielectric photonic crystal. Simulation space is implemented in the
first Brillouin zone, in order to obtain band structure and modal fields and in the supercell to
calculate waveguide modes. The Bloch theorem is used to implement fictitious periodic
boundary conditions for the first Brillouin zone and supercell. This method successfully
computes the transmission and reflection coefficients of photonic crystal waveguide without
significant error for termination of the computational space. To validate our code, the band
structure of a cubic lattice is simulated and results are compared with results of the plane wave
expansion method. The proposed method is shown to be applicable to photonic crystals of
irregular shape and frequency dependent (independent) materials, such as dielectric or dispersive
material, and experimental data for different lattice structures. Numerical calculations show that
the MMP method is stable, accurate and fast and can be used on personal computers.
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